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Heating and Heat Treatment
ArticleName Usage of the MathConnex mathematical package for thermotechnical calculation of heating furnaces
ArticleAuthor O. B. Kryuchkov, N. I. Gabelchenko, P. I. Malenko, L. G. Saranin

Volgograd State Technical University (Volgograd, Russia):

O. B. Kryuchkov, Cand. Eng., Deputy Dean, e-mail:
N. I. Gabelchenko, Cand. Eng., Associate Prof., e-mail:


Tula State University (Tula, Russia):
P. I. Malenko, Cand. Eng., Associate Prof., e-mail:
L. G. Saranin, Graduate Student, e-mail:


Abstract: In this work, for the thermotechnical calculation of continuous and chamber heating furnaces intended for heating billets for metal forming and heat treatment using the MathConnex mathematical package (part of MacCad Pro), flowcharts of a sectional furnace and a rolling hearth furnace have been presented that contain blocks with initial and output data, as well as calculation blocks: “fuel”, “heating time”, “heat balance”, “burner, nozzle”, “recuperator” and “chimney”. The flowcharts are “assembled” on a monitor screen using the previously developed abovementioned blocks by interactive means using the corresponding “palette” and are connected by arrows-links showing the paths for transmission of the initial and calculated data. For readability, blocks with initial data and output parameters are written in the form of Microsoft Excel tables, and calculation blocks are compiled on the basis of MatCad Pro, saturated with necessary programs, and data transmitted from other blocks that are written in the form of formulas are “encoded” and calculated. The proposed scheme of thermotechnical calculation allows to «automate» the calculations: composition of the furnace atmosphere, calorimetric and actual temperature of combustion products, thermophysical parameters of metal, masonry, Fourier criterion, temperature criteria of the surface and center of the metal; allows to solve various equations, including a system of equations for determining the temperature between layers in a multilayer masonry, calculating the heating time of billets, etc. The developed fl owcharts with the aim to optimize the technological process allow their multiple use for various initial data: fuel compositions, types of burners, nozzles and recuperators, schemes for laying billets on the furnace hearth, thicknesses and materials of masonry furnaces, etc. In addition, the MathConnex mathematical package (part of MattСad Pro) allows to analyze in detail, including, using graphing, parameters of interest due to the additional tools “Ramp”, “Conditional” and “Stop or Pause”: selection of the furnace temperature at the beginning of heating in order to eliminate the occurrence of dangerous temperature stresses in the heated metal; ways to reduce heat loss with combustion products leaving the furnace; compare the effect of ferrous metal emissivity factor on the emission reduced coefficient, combustion products and the degree of masonry development; to consider the effect of the method of billets laying in the furnace on time and uniformity of their heating; the influence of the air ratio and the nitrogen/ air oxygen ratio on the combustion products volume and others.

keywords MathConnex mathematical package (part of MаthCad Pro), heat engineering calculation (fuel, billet heating time, internal dimensions of the furnace, heat balance, burners, nozzles, recuperator, chimney), pusher, chamber, heating and thermal furnaces, thermophysical parameters of metal, masonry and furnace atmosphere

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